The second law of thermodynamics for high-energy channeled particles

In microscopic theory, the number of kinetic equations underlying the proof of the second law of thermodynamics is quite restricted. We explicitly prove that the second law of thermodynamics is satisfied for high-energy particles moving in a crystal in the channeling regime. The proof involves a local Boltzmann equation for the distribution function of the particles written in the Bogoliubov form. In this, we take one statistical mechanism into account: the scattering of channeled particles on lattice atoms randomly displaced from the crystal sites.